Quartic residues and binary quadratic forms

DOI10.1016/j.jnt.2004.11.003zbMath1101.11003OpenAlexW4212784737MaRDI QIDQ2566162

Zhi-Hong Sun

Publication date: 22 September 2005

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2004.11.003

zbMATH Keywords

binary quadratic formquartic Jacobi symbolquartic residue

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Power residues, reciprocity (11A15)

Related Items (11)

Cubic residues and binary quadratic forms ⋮ Residuacity and genus theory of forms ⋮ Values of Lucas sequences modulo primes ⋮ New reciprocity laws for octic residues and nonresidues ⋮ Quartic residues and sums involving \({4k}\choose{2k}\) ⋮ On the quadratic character of quadratic units ⋮ On the number of incongruent residues of \(x^4+ax^2+bx\) modulo \(p\) ⋮ On the existence of perfect splitter sets ⋮ Quartic, octic residues and Lucas sequences ⋮ Sun's conjectures on fourth powers in the class group of binary quadratic forms ⋮ Congruences for q^[p/8 (mod p) under the condition 4n²p = x² + qy²]

Cites Work

• Residuacity properties of real quadratic units
• Ring class fields modulo 8 of \({\mathbb{Q}}(\sqrt{-m})\) and the quartic character of units of \({\mathbb{Q}}(\sqrt{m})\) for m\(\equiv 1\) mod 8
• Konstruktion von Klassenkörpern und Potenzrestkriterien für quadratische Einheiten
• On the quartic character of certain quadratic units and the representation of primes by binary quadratic forms
• The quadratic and quartic character of certain quadratic units. I
• The quadratic and quartic character of certain quadratic units. II
• Values of Lucas sequences modulo primes
• Supplements to the theory of quartic residues
• On the quartic character of quadratic units.
• Fibonacci numbers and Fermat's last theorem
• Note on primes of type x2 + 32y2, class number, and residuacity.
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